On 21 Jul, 21:38, arithmonic <djes...@gmail.com> wrote: > On 16 jul, 04:39, "sttscitr...@tesco.net" <sttscitr...@tesco.net> > wrote: > > > I don't think the claim that these methods are in any way > > new stands up to scrutiny. > > The idea of Farey dissections is clearly not new. > > It is mentioned in Hardy and Wright for example. > . > > You mentioned "Farey Fractions". > Do you know what you are talking about? > and they operate only between TWO FRACTIONS (even when you can compute > many Mediants at the same time it always operate between TWO > FRACTIONS).
Again you reveal your profound ignorance in these matters. If you had read Hurwitz's paper you would realize that you can generalize Farey fractions to simultaneously approximate two irrationals, this involves either double or triple mediants.
> The paper you are mentioning deals only with best approximations to > any given number, but that is far from being a ROOT-SOLVING ALGORITHM.
If you approximate sqrt(2) you are solving x^2-2 =0
> The issue on "best approximations" is well explained on my web pages.
Then find the best simultaneous approximations to cubrt(25), cubrt(625).
I've made this simple challenge many times in the past and you were never able to meet it.
How can anyone believe what you say, if your methods cam't produce what you claim.